Simplify the following expression: $q = \dfrac{y}{10} \div \dfrac{9y}{4}$
Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{y}{10} \times \dfrac{4}{9y}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ y \times 4 } { 10 \times 9y}$ $q = \dfrac{4y}{90y}$ Simplify: $q = \dfrac{2}{45}$